The Complete Engineering Mechanics Course

Explore concurrent and coplanar forces in two-dimensional particle equilibrium. Learn to draw and label free body diagrams and apply the x- and y-equilibrium equations.

Master free body diagrams by labeling all forces, including magnitudes and distances, and determine tension or compression directions. Learn equilibrium, components, spring forces, and pulley implications for accurate force analysis.

Calculate the resultant moment of five forces using perpendicular distances and clockwise negative, anticlockwise positive conventions. Break the 7 N force into components and sum moments to determine rotation.

learn to compute the cross product on a calculator by defining two three-dimensional vectors, then applying the cross product to obtain the moment about a point in newton-meters.

Compute the moment of a force about point b using r_ba cross f, with r_ba = a−b, yielding m = 242 i + 182 j + 94 k N·m.

Compute the resultant moment from three couples using the perpendicular distances between force lines, sum the moments, and arrive at a final 490 newton-meters clockwise torque.

Learn to reduce a force and couple system to a single resultant force and moments about a point using scale analysis or vector analysis, determining magnitude and direction.

Further simplify a force and couple system on a disk in the x, y and z plane by replacing loading with an equivalent resultant force and its line-of-action coordinates.

Apply free body diagrams and equilibrium equations to determine the horizontal and vertical reactions at supports A and B in a two-dimensional rigid beam, using sums of forces and moments.

Identify two force members as equal in magnitude and opposite in direction, then draw free body diagrams and resolve the forces into x and y components and hinge components.

Apply the method of sections to a truss example, cutting through members DF, DG, GE, drawing a free body diagram, and solving equilibrium to identify tension or compression.

Apply the method of joints to determine forces in a simple truss, using free-body diagrams and equilibrium in x, y, and moments to identify tension or compression.

Explore frames and machines by analyzing joint forces with free body diagrams, applying equal and opposite components, solving with as many equations as unknowns, and using moments about intersection points.

Define the x and y axes and apply centroid formulas to compute coordinates of a workpiece’s centroid, using areas and positive or negative space for triangles, semicircles, arcs, and shapes.

Calculate the centroid of a composite metal piece by partitioning into rectangles, triangles, and a semicircle, then combine x and y centroids with area weights to locate the overall centroid.

Learn to compute internal forces in beams using the method of sections, drawing free body diagrams, and applying equilibrium with sign conventions for shear, normal force, and bending moment.

Draw the free-body diagram, apply the left-hand section with anticlockwise as positive, and derive the bending moment function M(x) for a beam with distributed loading.